VA_M.O.N.E.Y.: To add a couple of things to what rod said,
Think of a turn-based games site like way-back when people use to play chess by the mail. That is they would make a move, then send a postcard through the mail to someone who in turn made a move and sent them the move back and forth through the mail.
So a lot of people will sign on, make moves on the games they have, then leave the site. Then maybe the next day, they will sign back on and see what moves they have waiting for them.
Like rod mentioned, there are even faster time limits (like complete games within 1 hour), but in my opinion - if you like live games, there are other game sites out there that offer live games. But turn-based games might grow on you. Give it a try - that is, start some games - make your moves - then come back tomorrow and check to see what games have moves waiting.